px^(2)+(2q-p^(2))x-2pq=0ap+-0

If 25p^(2)+9q^(2)-r^(2)-30pq=0 a point on the line px+qy+r=0 is

If the roots of the equation x^(3) - px^(2) + qx - r = 0 are in A.P., then prove that, 2p^3 −9pq+27r=0

If alpha,beta are the roots of the equation px^(2)-qx+r=0, then the equation whose roots are alpha^(2)+(r)/(p) and beta^(2)+(r)/(p) is (i) p^(3)x^(2)+pq^(2)x+r=0 (ii) px^(2)-qx+r=0 (iii) p^(3)x^(2)-pq^(2)x+q^(2)r=0 (iv) px^(2)+qx-r=0

If alpha,beta are the roots of the equation x^(2)+px+q=0, then -(1)/(alpha),-(1)/(beta) are the roots of the equation x^(2)-px+q=0 (b) x^(2)+px+q=0( c) qx^(2)+px+1=0 (d) q^(2)-px+1=0

If p, q, r are rational then show that x^(2)-2px+p^(2)-q^(2)+2qr-r^(2)=0

If p. q are odd integers. Then the roots of the equation 2px^(2)+(2p+q)x+q=0 are